In a medium saucepan, place the apple juice, cinnamon, and cardamom, and bring the mixture to a boil. Reduce the heat to low and simmer for 7 minutes. Add the remaining ingredients and simmer the mixture an additional 5 minutes. Remove the saucepan from the heat. Transfer half of the mixture to a blender or food processor and process for 1-2 minutes or until smooth. Add the pureed mixture back to the saucepan and stir well to combine. Serve the syrup warm or at room temperature over pancakes, French toast, waffles, and other breakfast items, as a topping for fresh fruit, or use a sauce for desserts.